Black-holes, topological strings and large N phase transitions

The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${\mathcal O}(p-2)\oplus{\mathcal O}(-p) \longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.Comment: 16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy), September 200

Phase transitions, double-scaling limit, and topological strings

Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q--deformed 2d Yang--Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2d gravity. We give strong evidence that there is a double--scaled theory at the critical point whose all genus free energy is governed by the Painlev\'e I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2d supergravity. We also give evidence for a new open/closed duality relating these Calabi--Yau backgrounds to open strings with framing.Comment: 49 pages, 3 eps figures; section added on non-perturbative proposal and 2d gravity; minor typos correcte

Flips, dualities and symmetry enhancements

Abstract We present various 4d $$\mathcal{N}$$ N = 1 theories enjoying IR global symmetry enhancement. The models we consider have the USp(2N) gauge group, 8 fundamental, one antisymmetric chirals and various numbers of gauge singlets. By suitably turning on superpotential deformations involving the singlets which break part of the UV symmetry we flow to SCFTs with E6, SO(10), SO(9), SO(8) and F4 IR global symmetry. We explain these patterns of symmetry enhancement following two arguments due to Razamat, Sela and Zafrir. The first one involves the study of the relations satisfied by marginal operators, while the second one relies on the existence of self-duality frames.</jats:p

Localization techniques in quantum field theories

This is the foreword to the special issue on localization techniques in quantum field theory. The summary of individual chapters is given and their interrelation is discussed

\Omega-deformation of B-twisted gauge theories and the 3d-3d correspondence

We study \Omega-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an \Omega-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface $\Sigma$ and a three-manifold $M$, and show that when $\Sigma$ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on $M$. Based on these results, we establish a correspondence between three-dimensional $\mathcal{N} = 2$ superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between {\Omega}-deformed two-dimensional theories.Comment: 26 pages. v2: the discussion on the boundary condition for vector multiplet improved, and other minor changes mad

Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED

We re-examine the perturbative properties of four-dimensional non-commutative QED by extending the pinch techniques to the theta-deformed case. The explicit independence of the pinched gluon self-energy from gauge-fixing parameters, and the absence of unphysical thresholds in the resummed propagators permits a complete check of the optical theorem for the off-shell two-point function. The known anomalous (tachyonic) dispersion relations are recovered within this framework, as well as their improved version in the (softly broken) SUSY case. These applications should be considered as a first step in constructing gauge-invariant truncations of the Schwinger-Dyson equations in the non-commutative case. An interesting result of our formalism appears when considering the theory in two dimensions: we observe a finite gauge-invariant contribution to the photon mass because of a novel incarnation of IR/UV mixing, which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde

Urban informality and confinement: toward a relational framework

In the 21st century, a growing number of people live ‘informal’ lives within fissures between legality and informality. Concomitantly, power relations are increasingly expressed through devices of confinement. While urban informality and confinement are on the rise often occurring simultaneously, scholars have so far studied them separately. By contrast, this article proposes a new framework for analysing urban informality and confinement relationally. It generates new insights into the role of informality in the (re)production of confinement and, vice versa, the role of confinement in shaping informal practices. While these insights are valuable for urban studies in general, the article charts new lines of research on urban marginality. It also discusses how the six articles included in this special issue signal the heuristic potential of this relational framework by empirically examining distinct urban configurations of ‘confined informalities’ and ‘informal confinements’ across the Global North and the Global South

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.Comment: 30 pages, 4 figures. v2: typo corrected, references adde

Nonperturbative aspects of ABJM theory

Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published in JHE